USING C++

Design and construct a computer program in (C++) that will illustrate the effects of rounding errors and truncation errors. Also, note that the arguments of all trigonometric functions in this course are measured in radians.

The following is a plot of the function f(x) = sin(x³) + x²

In order to illustrate the effects of the two major error sources, rounding and truncation, attempt to determine an approximation to the derivative of f(x) at x = 1.0 radians using the difference approximation given below. (The true answer is 2 + 3 cos(1) or about 3.620906917604419152202810).

Use the formula:

f'(x) (f(x+h) - f(x)) / h

with h=1, 0.5, 0.25, ... 1.8189894035459e-12

(i.e., keep halving h until it is less than 2.0e-12.)

Print out the values of h, your approximation to f'(x), and the error in the approximation for each value of hused. This error will include the effects of both truncation and rounding.